Adaptive RBF -SMC control for multi-point mooring system

A stable adaptive control scheme for multi-point mooring system (MPMS) with uncertain dynamics is proposed in this paper. The control scheme is designed by a hybrid controller based on RBF (Radial Basis Function) NN (Neural Network) and SMC (Sliding Mode Control), which learns the MPMS dynamic changes, and the compensation of external disturbances is realized through adaptive RBFNN control. Meanwhile the RBF-SMC control parameters are adapted by the Lyapunov method to minimize squares dynamic positioning (DP) error. The convergence of the hybrid controller is proved theoretically, and the proposed mooring control scheme is applied to the “Kantan3” mooring simulation system. Finally, the simulation results are compared with the traditional PID controller and standard RBF controller to demonstrate the effective mooring positioning performance of the control scheme for the MPMS.

Investigating errors when forecasting processes with uncertain dynamics and observation noise by the self-adjusting brown's zero-order model

This paper reports a study into the errors of process forecasting under the conditions of uncertainty in the dynamics and observation noise using a self-adjusting Brown's zero-order model. The dynamics test models have been built for predicted processes and observation noises, which make it possible to investigate forecasting errors for the self-adjusting and adaptive models. The test process dynamics were determined in the form of a rectangular video pulse with a fixed unit amplitude, a radio pulse of the harmonic process with an amplitude attenuated exponentially, as well as a video pulse with amplitude increasing exponentially. As a model of observation noise, an additive discrete Gaussian process with zero mean and variable value of the mean square deviation was considered. It was established that for small values of the mean square deviation of observation noise, a self-adjusting model under the conditions of dynamics uncertainty produces a smaller error in the process forecast. For the test jump-like dynamics of the process, the variance of the forecast error was less than 1 %. At the same time, for the adaptive model, with an adaptation parameter from the classical and beyond-the-limit sets, the variance of the error was about 20 % and 5 %, respectively. With significant observation noises, the variance of the error in the forecast of the test process dynamics for the self-adjusting and adaptive models with a parameter from the classical set was in the range from 1 % to 20 %. However, for the adaptive model, with a parameter from the beyond-the-limit set, the variance of the prediction error was close to 100 % for all test models. It was established that with an increase in the mean square deviation of observation noise, there is greater masking of the predicted test process dynamics, leading to an increase in the variance of the forecast error when using a self-adjusting model. This is the price for predicting processes with uncertain dynamics and observation noises.

Fixed-Time Adaptive Neural Network Tracking Control for Output-Constrained High-Order Systems Using Command Filtered Strategy

This paper proposes a fixed time adaptive neural command filtered controller for a category of high-order systems based on adding a power integrator technique. Different from existing research, the presented controller has the following distinguishing advantages: i) fixed-time control framework is extended to the tracking control problem of high-order systems. ii) the error compensation mechanism eliminates filter errors that arise from dynamic controllers. iii) growth assumptions about unknown functions are relaxed with the help of adaptive neural networks. iv) more general systems: the developed controller can apply to high-order systems subject to uncertain dynamics, unknown gain functions and asymmetric constraints. Stability analysis shows that all states are semi-globally bounded, and the convergence rate of tracking error is independent of initial conditions. The main innovation of our work is that the presented controller considers simultaneously filter errors, fixed-time convergence, growth conditions and asymmetric output constraint for the tracking control issue of high-order systems. Finally, the simulation results validate the advantages and efficacy of the developed control scheme.

Nonlinear burn control in ITER using adaptive allocation of actuators with uncertain dynamics

ITER will be the first tokamak to sustain a fusion-producing, or burning, plasma. If the plasma temperature were to inadvertently rise in this burning regime, the positive correlation between temperature and the fusion reaction rate would establish a destabilizing positive feedback loop. Careful regulation of the plasma’s temperature and density, or burn control, is required to prevent these potentially reactor-damaging thermal excursions, neutralize disturbances and improve performance. In this work, a Lyapunov-based burn controller is designed using a full zero-dimensional nonlinear model. An adaptive estimator manages destabilizing uncertainties in the plasma confinement properties and the particle recycling conditions (caused by plasma-wall interactions). The controller regulates the plasma density with requests for deuterium and tritium particle injections. In ITER-like plasmas, the fusion-born alpha particles will primarily heat the plasma electrons, resulting in different electron and ion temperatures in the core. By considering separate response models for the electron and ion energies, the proposed controller can independently regulate the electron and ion temperatures by requesting that different amounts of auxiliary power be delivered to the electrons and ions. These two commands for a specific control effort (electron and ion heating) are sent to an actuator allocation module that optimally maps them to the heating actuators available to ITER: an electron cyclotron heating system (20 MW), an ion cyclotron heating system (20 MW), and two neutral beam injectors (16.5 MW each). Two different actuator allocators are presented in this work. The first actuator allocator finds the optimal mapping by solving a convex quadratic program that includes actuator saturation and rate limits. It is nonadaptive and assumes that the mapping between the commanded control efforts and the allocated actuators (i.e., the effector model) contains no uncertainties. The second actuator allocation module has an adaptive estimator to handle uncertainties in the effector model. This uncertainty includes actuator efficiencies, the fractions of neutral beam heating that are deposited into the plasma electrons and ions, and the tritium concentration of the fueling pellets. Furthermore, the adaptive allocator considers actuator dynamics (actuation lag) that contain uncertainty. This adaptive allocation algorithm is more computationally efficient than the aforementioned nonadaptive allocator because it is computed using dynamic update laws so that finding the solution to a static optimization problem is not required at every time step. A simulation study assesses the performance of the proposed adaptive burn controller augmented with each of the actuator allocation modules.

Encouraging Volitional Pedaling in Functional Electrical Stimulation-Assisted Cycling Using Barrier Functions

Stationary motorized cycling assisted by functional electrical stimulation (FES) is a popular therapy for people with movement impairments. Maximizing volitional contributions from the rider of the cycle can lead to long-term benefits like increased muscular strength and cardiovascular endurance. This paper develops a combined motor and FES control system that tasks the rider with maintaining their cadence near a target point using their own volition, while assistance or resistance is applied gradually as their cadence approaches the lower or upper boundary, respectively, of a user-defined safe range. Safety-ensuring barrier functions are used to guarantee that the rider’s cadence is constrained to the safe range, while minimal assistance is provided within the range to maximize effort by the rider. FES stimulation is applied before electric motor assistance to further increase power output from the rider. To account for uncertain dynamics, barrier function methods are combined with robust control tools from Lyapunov theory to develop controllers that guarantee safety in the worst-case. Because of the intermittent nature of FES stimulation, the closed-loop system is modeled as a hybrid system to certify that the set of states for which the cadence is in the safe range is asymptotically stable. The performance of the developed control method is demonstrated experimentally on five participants. The barrier function controller constrained the riders’ cadence in a range of 50 ± 5 RPM with an average cadence standard deviation of 1.4 RPM for a protocol where cadence with minimal variance was prioritized and used minimal assistance from the motor (4.1% of trial duration) in a separate protocol where power output from the rider was prioritized.

Corrigendum to “Chaos in a Financial System with Fractional Order and Its Control via Sliding Mode”

In this paper, the dynamical behaviors and chaos control of a fractional-order financial system are discussed. The lowest fractional order found from which the system generates chaos is 2.49 for the commensurate order case and 2.57 for the incommensurate order case. Also, the period-doubling route to chaos was found in this system. The results of this study were validated by the existence of a positive Lyapunov exponent. Besides, in order to control chaos in this fractional-order financial system with uncertain dynamics, a sliding mode controller is derived. The proposed controller stabilizes the commensurate and incommensurate fractional-order systems. Numerical simulations are carried out to verify the analytical results.

Adaptive Critic Learning-Based Robust Control of Systems with Uncertain Dynamics

Model uncertainties are usually unavoidable in the control systems, which are caused by imperfect system modeling, disturbances, and nonsmooth dynamics. This paper presents a novel method to address the robust control problem for uncertain systems. The original robust control problem of the uncertain system is first transformed into an optimal control of nominal system via selecting the appropriate cost function. Then, we develop an adaptive critic leaning algorithm to learn online the optimal control solution, where only the critic neural network (NN) is used, and the actor NN widely used in the existing methods is removed. Finally, the feasibility analysis of the control algorithm is given in the paper. Simulation results are given to show the availability of the presented control method.